Question

Which graph represents the following piecewise defined function?

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

The correct answer is shown in attached figure
To find the correct graph, we should study the continuity of the function

Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2

Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3


From the previous results the correct graph is the last as shown in attached graph.